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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">X0</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="tsp_2.html#NM1" title="TSP_2:NM.1">maximal_Kolmogorov_subspace</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> holds  <span class="p1">(<span class="default"><a href="tsp_2.html#K4" title="TSP_2:func.4">Stone-retraction</a> <font color="Maroon" title="c1">X</font>,<font color="Olive" title="b1">X0</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="tsp_2.html#K4" title="TSP_2:func.4">Stone-retraction</a> <font color="Maroon" title="c1">X</font>,<font color="Olive" title="b1">X0</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Olive" title="b2">A</font></span><br/><b>let </b><font color="Maroon" title="c2">X0</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="tsp_2.html#NM1" title="TSP_2:NM.1">maximal_Kolmogorov_subspace</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> holds  <span class="p1">(<span class="default"><a href="tsp_2.html#K4" title="TSP_2:func.4">Stone-retraction</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">X0</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="tsp_2.html#K4" title="TSP_2:func.4">Stone-retraction</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">X0</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Olive" title="b1">A</font></span><br/><b>let </b><font color="Maroon" title="c3">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="tsp_2.html#K4" title="TSP_2:func.4">Stone-retraction</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">X0</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="tsp_2.html#K4" title="TSP_2:func.4">Stone-retraction</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">X0</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c3">A</font></span><br/>





<b>reconsider </b><font color="Maroon" title="c4">C</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X0</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="tsep_1.html#T1" title="TSEP_1:th.1">TSEP_1:1</a></i>;<br/>
<b>set </b><font color="Maroon" title="c5">r</font> =  <a href="tsp_2.html#K4" title="TSP_2:func.4">Stone-retraction</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">X0</font>;<br/>
<a NAME="E2:49"/>
<font color="Maroon" title="c4">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>
 
;<br/>
<b>then reconsider </b><font color="Maroon" title="c6">B</font> = <span class="p1">(<span class="default"><a href="tsp_2.html#K4" title="TSP_2:func.4">Stone-retraction</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">X0</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">A</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E4:49"/><i><font color="Green" title="E36">A1</font></i>: 
<span class="p1">(<span class="default"><a href="tsp_2.html#K4" title="TSP_2:func.4">Stone-retraction</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">X0</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="tsp_2.html#K4" title="TSP_2:func.4">Stone-retraction</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">X0</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c6">B</font>
 
<b>by </b><i><a class="ref" href="tsp_2.html#T26" target="_self" title="TSP_2:th.26">Th26</a></i>;<br/>
<a NAME="E5:49"/><b>then </b><i><font color="Green" title="E37">A2</font></i>: 
<font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c6">B</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T50" title="FUNCT_2:th.50">FUNCT_2:50</a></i>;<br/>
<a NAME="E6:49"/>
<font color="Maroon" title="c4">C</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">B</font>
 
<b>by </b><i><a class="ref" href="tsp_2.html#D12" target="_self" title="TSP_2:def.12">Def12</a></i>;<br/>
<a NAME="E7:49"/><b>then </b>
<font color="Maroon" title="c6">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c3">A</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/>
<b>hence </b><a NAME="E8:49"/>
<span class="p1">(<span class="default"><a href="tsp_2.html#K4" title="TSP_2:func.4">Stone-retraction</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">X0</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="tsp_2.html#K4" title="TSP_2:func.4">Stone-retraction</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">X0</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tex_4.html#K3" title="TEX_4:func.3">MaxADSet</a> <font color="Maroon" title="c3">A</font>
 <b>by </b><i><a class="txt" href="tsp_2.html#E4:49"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="tsp_2.html#E5:49"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="tex_4.html#T37" title="TEX_4:th.37">TEX_4:37</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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